g(x) as given has no inverse because there are instances of two x values giving the same value of g(x). For instance,
x = -1 ⇒ g(-1) = 4 (-1 + 3)² - 8 = 8
x = -5 ⇒ g(-5) = 4 (-5 + 3)² - 8 = 8
Only a one-to-one function can have an inverse. g(x) is not one-to-one.
However, if we restrict the domain of g(x), we can find an inverse over that domain. Let be the inverse of g(x). Then by definition of inverse function,
Solve for the inverse:
Recall the definition of absolute value:
This means there are two possible solutions for the inverse of g(x) :
• if , then
• otherwise, if , then
Which we choose as the inverse depends on how we restrict the domain of g(x). For example:
Remember that the inverse must satisfy
In the first case above, , or . This suggests that we could restrict the domain of g(x) to be .
Then as long as , the inverse is
Answer:
The true solution of given polynomial is 1.732 , - 1.732
Step-by-step explanation:
Given polynomial as :
=
Or, =
Or, =
Taking away 2 as common from denominator of both side
So, =
Now, cross multiplying both side
Or, x² × (x - 3) = 3 × (x - 3)
Or, =
Or, = 1
∴ x² = 3
i.e x =
Or, x = 1.732 , and x = - 1.732
So, The value of x = 1.732 , - 1.732
Hence, The true solution of given polynomial is 1.732 , - 1.732 Answer
Answer:
Just substitute x with 3.the answer should be - 26.
Step-by-step explanation:
Answer:
y=-2x+4
Step-by-step explanation:
Answer:
The correct answer is B. 51.165